Exercise "math"

1. Calculate, using mathematical functions form <math.h> and <complex.h> (or <tgmath.h>); :
   • Gamma function Γ(5). Hint: man -k gamma.
   • Bessel function J₁(0.5). Hint: man -k bessel.
   • √-2, e^iπ, eⁱ, i^e, iⁱ, and check that the results are correct.

   Hints:

   • There is no built-in format for complex numbers, you have to print separately the real and the complex parts using creal, creall, cimag, cimagl functions; read man creal and man cimag.
   • The header file complex.h defines the imaginary unit as I.
   • In some implementations the header math.h defines M_E (the value of e) and M_PI (the value of π). If not, you can define this constants (in double precision) as

     # define M_E  2.7182818284590452354 /* e */
     # define M_PI 3.1415926535897932384 /* pi */
     

2. Find out how many signigicant digits can variables of types float, double, and long double hold in them by calculating the ratio 1/9 with the corresponding precision and then printing out the result. Something like

   float x_float = 1.f/9;
   double x_double = 1./9;
   long double x_long_double = 1.L/9;
   

   Print these numbers with format placeholders "%.25g" for float, "%.25lg" for double, "%.25Lg" for long double.